Apparatus for tracking connection of service provider customers via customer use patterns

ABSTRACT

A method for identifying tracking accounts belonging to a customer of a service provider using profiles indicating customer patterns of use of the service. The profiles distinguish the account of the service provider customers from each other. Those profiles that substantially match are considered to belong to the same customer.

RELATED APPLICATION

This is a continuation application of U.S. patent application filed Aug.30, 2000, bearing the Ser. No. 09/650,634 now U.S. Pat. No. 6,700,960,which is hereby incorporated by reference.

TECHNICAL FIELD

The present invention relates to a method and apparatus for obtaininginformation on service provider customers and, more particularly, to amethod and apparatus for tracking customer connection to a serviceprovider using customer profiles indicating customer use patterns.

BACKGROUND OF THE INVENTION

It is not uncommon for a customer of a service provider, such as anInternet service provider or a long-distance telephone service provider,to obtain and maintain multiple accounts, either simultaneously or atdifferent periods of time. Service providers often find it desirable tomatch such multiple customer accounts with the single customer. Thiscustomer identification enables the service provider to ensurecontinuity in the type of service provided to the customer, to identifyhighly valued customers and/or to identify less desirable customers orcustomers with delinquent accounts. Traditional information, such asname and address, are usually used to perform the customer accountmatching. This method of account matching suffers from certaindisadvantages.

More particularly, it is often difficult for the service providers toperform the account matching on their own existing data. Therefore,service providers usually provide account information to outside vendorswho are paid to perform matching against their databases. Since theservice providers cannot utilize existing data to perform the matching,they must incur the cost of hiring outside vendors to perform the task.In addition, it is often difficult for the outside vendors to matchmultiple accounts belonging to a single customer using traditionalidentifying information, since this information is often entereddifferently for each account and is subject to frequent errors in dataentry. In sum, this method for customer account matching is costly, andoften inaccurate.

Therefore, a method and apparatus for tracking the connection ofcustomers of a service provider are needed which would enable theservice provider to easily and accurately track customer movement orconnection. The present invention was developed to accomplish these andother objectives.

SUMMARY OF THE INVENTION

In view of the foregoing, it is a principal object of the presentinvention to provide a method and apparatus that eliminates thedeficiencies of the prior art.

It is a further object of the present invention to provide a method andapparatus for accurately tracking movement and/or connection of serviceprovider customers by accurately matching multiple accounts belonging toa single customer.

It is yet another object of the present invention to provide a methodand apparatus for accurately matching multiple accounts belonging to asingle customer by identifying customers based upon patterns in customeruse of the service.

It is a further object of the present invention to provide a method andapparatus for accurately matching multiple accounts belonging to asingle customer by comparing the pattern of use of a particular accountwith the patterns of use for each of the remaining accounts of theservice, and identifying multiple accounts as belonging to a singlecustomer when the pattern of use for the particular accountsubstantially matches the pattern of use of at least one of theremaining accounts.

It is a further object of the present invention to provide a method andapparatus for accurately matching multiple accounts belonging to asingle customer by comparing the pattern of use of each account in afirst sample of accounts being investigated with the pattern of use foreach of the accounts constituting a second sample of accounts of theservice provider, and determining that an account in the first sample ofaccounts and at least one account in the second sample of accountsbelong to a single customer when the pattern of use for the account inthe first sample of accounts substantially matches the pattern of use ofat least one of the accounts in the second sample of customers.

It is a further object of the present invention to provide a method andapparatus for accurately matching multiple accounts belonging to asingle customer by comparing the pattern of use of each of the accountsin a first sample of accounts being investigated with the patterns ofuse for each of the accounts constituting a second sample of accounts ofthe service provider, where the second sample of accounts constitutes asubset of all of the accounts of the service provider, and determiningthat an account in the first sample of accounts and at least one accountin the second sample of accounts belong to a single customer when thepattern of use of the account substantially matches the pattern of useof at least one of the accounts in the second sample of customers.

It is yet another object of the present invention to provide a methodand apparatus for assigning customer history information to multipleaccounts belonging to a single customer by comparing the pattern of useof a particular account of the single customer with the pattern of usefor the remaining accounts, identifying multiple accounts as belongingto the single customer when the pattern of use for the particularaccount substantially matches the pattern of use of at least one of theremaining accounts, and assigning the customer history information ofthe matching remaining account(s) to the particular account.

These and other objects and features of the present invention will beapparent upon consideration of the following detailed description ofpreferred embodiments thereof, presented in connection with thefollowing drawings in which like reference numerals identify likeelements throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings,

FIG. 1 illustrates an example of a telecommunications system;

FIG. 2 illustrates the basic elements of a system for performing themethod according to the present invention;

FIG. 3 illustrates a flow diagram of the steps performed in the methodaccording to the present invention;

FIG. 4 illustrates an example of customers of a service provider and theinformation obtained from the customers for performing the methodaccording to the present invention;

FIG. 5 illustrates an example of how one customer account isdistinguished from the remaining customer accounts in a sample accordingto the present invention; and

FIG. 6 illustrates another example of how of how one customer account isdistinguished from the remaining customer accounts in a sample accordingto the present invention.

DETAILED DESCRIPTION OF THE INVENTION

In order to facilitate the description of the present invention, theinvention will be described with respect to the particular example oflong-distance telephone service providers. Examples will be describedthat illustrate particular applications of the invention forlong-distance telephone service. The present invention, however, is notlimited to any particular service provider nor limited by the examplesdescribed herein. Therefore, the description of the embodiment thatfollows is for purposes of illustration and not limitation.

A particular application of the present invention is identifyingcustomers of a long-distance telephone service provider who have movedwithout informing the long-distance telephone service provider. Theidentification is accomplished by matching the customer's pre-move andpost-move calling patterns. For example, upon moving, a customer usuallynotifies their local telephone service provider to disconnect theirservice and close their account, and reconnect and open another accountat the new location. The customer often assumes that their long-distanceservice provider will be notified and will be able to match their newaccount with their past history. However, the information provided tothe long-distance provider from the local service provider does notdistinguish a “mover” from a “new connect”. Therefore, the long-distanceprovider cannot match the new account with the past history of thecustomer.

Another application of the invention with respect to long-distancetelephone service providers is to identify a customer who has openedmultiple accounts with different names or where the names have beenentered differently by a data entry person (e.g., one account underJoseph Smith and another account under Ellen Smith or one account underJoseph Smith and another account under J. Smith). The present inventionsolves these and other problems by using customer calling pattern datato match multiple accounts belonging to a single customer.

Referring to FIG. 1, an exemplary telecommunications network 10 isshown. Local switching offices 12 and 14 are connected to each other bytrunk 20, while local switching offices 16 and 18 are connected to eachother by trunk 22. Trunk 20 is used to route calls from a telephone 26served by the local switching office 12 to a telephone 28 serviced bythe terminating local switching office 14. Long-distance calls totelephone 32, for example, are processed by a long-distance network 30.Service within local access and transport areas for local calls is oftenprovided by local telephone exchange carriers such as Bell South, andservice between the local access and transport areas for long-distancecalls is often provided by interexchange carriers such as AT&T.

FIG. 2 illustrates the basic elements of a system for performing themethod according to the present invention. A data processing system 34receives the customer use detail information for each customer viainterface 33. The data processing system 34 uses the use detailinformation for each customer to generate customer profiles todistinguish customers from one another. The data processing system 34outputs a profile for each service provider customer based upon serviceuse patterns. In addition, it performs the account comparison step andoutputs probable matches based upon the result of the comparison, aswell as the overlapping information associated with the probable match.The output from the data processing system 34 may be supplied to amonitor 35, printer 36, and/or other output device 37. The customer usedata information may be obtained by any appropriate means utilized bythe service provider.

According to the example of the present invention described herein,customers are characterized by the calls they make on the long-distancenetwork 30. The long-distance telephone service provider records callinformation for billing purposes. This data is recorded at a very lowerror rate. This data may include the telephone number making the call,the telephone number being called, the time of day, and/or the durationof the call, for example. This existing data may be used as call detailinformation to determine the call patterns of the service providercustomers. The call patterns may then be used to identify multipleaccounts belonging to a single customer. Therefore, no outside vendorservices are required to perform the present invention.

A customer's calling use is, of course, variable, but the presentinvention exploits the fact that people tend to call certain numbers(e.g., family) repeatedly over time. By identifying customers oraccounts by groups of called numbers, the method according to thepresent invention is robust to variations in calling pattern over time.The general procedure is described below with reference to FIG. 3.

First, depending on the purpose of the matching, a sample of knowncustomers of interest is identified in steps S1 and S2. The sample mayinclude all of the service provider customers or a subset of the serviceprovider customers. For example, if the service provider is trying todetect when a new account belongs to a high-value customer who recentlymoved without informing the service provider, the sample consists ofhigh-value customers who disconnected from the service provider at aboutthe same time that a new account(s) was opened. Then, the serviceprovider obtains the list of all calls to or from the customers in thesample over a chosen time period, e.g., one or two months, as shown instep S3. In step S4, the service provider aggregates any customer callsto or from a single number into a “feature.” The service providereliminates from the set of features all calls that are relativelyfrequent across the sample with respect to an experimentally chosenthreshold. For example, if many of the customers in the sample called amajor catalog merchant, the merchant's number has little power fordistinguishing one customer from another, and it is ignored. The nextstep is to construct a profile or “fingerprint” for each customer in thesample, i.e., a subset of the features attributed to the customer, sothat any two customers in the sample have different profiles (althoughtheir profiles may have some features in common), as shown in step S5.

Feature selection and profiling are also performed for each of theaccounts being investigated (continuing with the movers example, the setof new accounts connected to the service provider), as shown in stepsS6–S10 for identifying customers in a second sample of accounts to belater compared to the first sample in steps S1–S5. The comparison foraccount matching of the first sample of accounts to the second sample ofaccounts is performed in step S1 to look for accounts in the two samplesthat have similar fingerprints. In step S12, probable matches aredetermined in accordance with the results of the comparison in step S11.

The method according to the present invention is not hindered by minorchanges in customer use, because the method does not require identicalfingerprints for a match. The matched accounts may not be for the samecustomer, but they have a relatively high probability of being so, andare cost-effective targets for further investigation, such as bycontacting the customer directly.

The method and apparatus according to the present invention providesnumerous advantages to the service provider. More specifically, theinformation obtained by the matching method and apparatus may be used toprovide continuity of service to customers and to identify high-valuecustomers. In addition, the information may be used to screen newaccounts for creditworthiness. If a new customer's call pattern matchesan old account with a history of delinquency or fraud, the serviceprovider would have the opportunity to restrict the new account,avoiding the generation of new uncollectible debt. The service providermay also use the information to pursue collection of an old account'sdebt, gaining revenue that would otherwise be lost.

A more detailed description of the method and apparatus according to thepresent invention as implemented in the telecommunications example isset forth below.

Phase I. Profiling Customers

A long-distance customer's calling activity includes a sequence ofinbound and outbound calls. Those calls have a number of attributes,such as duration, time of day, time of week, etc. If a customer'scalling activity is observed over some time window, additionalattributes can be derived. Derived attributes may include frequency ofcalls made by the customer to a particular number, average talk time,total talk time, etc. It will be appreciated by those of ordinary skillin the art that many different attributes and derived attributes arepossible.

In the example illustrated in FIG. 4, customers A and B are subscribersof a particular long-distance telephone service provider. Customer C isnot a subscriber to the particular long-distance provider. Assume thatcustomer A is a member of a first sample of customers representing thecustomers to be investigated. The first sample may be a subset of all ofthe service provider customers. For example, assume that the firstsample of customers includes high value customers who disconnected fromthe service provider around the time that a new connection(s) occurred.Also assume that the profiles of the customers in this sample, includingthe profile of customer A, will be matched or compared against theprofiles of the service provider customers constituting a second sampleof customers. In the present example, assume that the second samplerepresents new account(s) of the service provider.

In order to create a profile for customer A, customer A's call patternfor some period of time is monitored. The period of time may be selectedby the service provider and need only be long enough to observe acalling pattern. Step S20 in FIG. 4 illustrates the step of recordinginformation for each of customer A's calls. In the current example, theinformation recorded for customer A includes the number making the call,the number being called, the time of day, and the duration of the call.Of course, the recorded information may include more or less informationor different information than that shown in the example of FIG. 4.

A profile for customer A is generated from the recorded information, asshown in step S21. More particularly, for each of customer A's calls,the call's frequency within the period of time may be determined. Inaddition, each call may be distinguished as either an inbound call or anoutbound call. In this framework, customer A's call detail may bedefined by a set of features (phone numbers), each determined uniquelyby a number called and a direction (inbound/outbound). More formally, afeature of customer A may be defined to be the pair:f=(c, I/O indicator)where f=a feature (Billed Telephone Number (BTN)); c=number (BTN) calledby A (outbound call) or the number (BTN) which called A (inbound call);and the I/O indicator=1 for inbound calls or 0 for outbound calls. Also,let the frequency φ_(Af) be the ratio of calls A made (received) to(from) c relative to all calls A made (received).

Customer A is identified by its BTN. Calls c are identified by theirBTNs as well. If an outbound call is made by A to c, c doesn't even haveto be a customer of the service provider. For example, in FIG. 4,customer A may place a call to customer C, who is not a customer of theparticular service provider (i.e., customers A and C subscribe todifferent long-distance telephone service providers). All calls passingthrough A's service provider's network are observed. Therefore, the datafor creating the customer profile will include all calls made bycustomer A, even if the recipient is not a customer of the serviceprovider. The reverse is not true, however, because a call from anon-subscriber may reach customer A without touching the serviceprovider network to which customer A subscribes. Therefore, for inboundcalls, only calls coming from the customers of the service provider towhich A subscribes are observed. In FIG. 4, this means that only callsfrom customer B to customer A are observed, as shown in Step S21. Thesteps shown in FIG. 4 correspond to steps S1–S4 in FIG. 3.

The list of features of customer A can be large, consisting of all callsthat “touched” customer A in the given time window. Some of those callsmay be incidental, while some may be part of a consistent patternspecific to customer A. The goal of profiling is to substantially reducethe number of features to be included in customer A's profile, and stillbe able to differentiate between customer A and all other customers inthe sample. Therefore, features that are incidental may be eliminated.This may be accomplished by selecting a frequency threshold τ_(f), andincluding feature f in the list of features for customer A only if thefrequency φ_(Af) exceeds the frequency threshold τ_(f). In calculatingthe threshold τ_(f), only calls to/from customers in the sample ofprofiled customers are considered. Therefore τ_(f) is based on thesample data. The threshold can be selected based upon experience of theservice provider, on experiments performed by the service provider orbased on training. The threshold varies depending upon the serviceprovider and on the needs of the service provider. Therefore, anysuitable method for selecting the threshold may be used. The goal is tocreate a calling profile or “fingerprint” for customer A, as shown instep S5 in FIG. 3, such that:

-   (i) the profile allows the service provider to distinguish customer    A from all the other customers in the sample;-   (ii) the profile consists of as few features as possible;-   (iii) the features in the profile either are unique to customer A or    appear on the feature list of as few other customers as possible;    and-   (iv) the features in the profile are with high probability a part of    customer A's typical pattern.    Step (iv) can be accomplished by limiting feature inclusion with    appropriate thresholds on φ_(Af), while steps (i), (ii) and (iii)    can be accomplished with an integer optimization model of set    covering, as discussed below.    Set Covering Problem According to a First Embodiment

For any set S, let |S| represent the number of members of S. Let the setΩ be the first sample of customers, with |Ω|=m+1. Let AεΩ be a customerto be profiled, and let F_(A) be the list of all features f of customerA whose frequencies φ_(Af) pass their associated thresholds τ_(f). Letn=|F_(A)|. Consider customer BεΩ, B≠A. Customer A's pattern isdetermined to differ significantly from customer B's with respect tofeature f if one of the two passes threshold τ_(f) and the other doesnot, i.e.,A≠ _(f) B if and only if φ_(Af)>τ_(f) and φ_(Bf)≦τ_(f) (or vice versa).For every feature f from the list F_(A), create a set S_(f)={B:φ_(Bf)≦τ_(f)}. S_(f) is the subset of Ω such that B εS_(f) if and onlyif A≠_(f)B. Then

S_(f) is the set of all customers in Ω that differ significantly fromcustomer A on at least one feature. Assume that

S_(f)=Ω\A; that is, no customer other than customer A has a list offeatures identical with customer A. It follows, that |

S_(f)|=m. The problem of minimizing the number of features used todistinguish customer A can be formulated as minimizing the number ofsets S_(f) needed to cover Ω\A, as follows:

-   Let a_(Bf)=1 if B εS_(f), and 0 otherwise.-   Let x_(f)=1 if f is selected, and 0 otherwise.    minimize

$\sum\limits_{f = 1}^{n}\; x_{f}$subject to

${\sum\limits_{f = 1}^{n}{a_{{B\; f}\;}\; x_{f}}} \geq 1$for B=1, . . . , mand x_(f)=0 or 1 for f εF_(A).Given the optimal solution x*, cover F*={f: x_(f)*=1} provides a minimalset of features establishing customer A as distinctly different fromeach customer B in the sample to be investigated. This integer programis an example of the set covering problem.Greedy Algorithm

The set covering problem can be solved for each customer. When there area large number of customers (e.g., 1.5 million) disconnecting eachmonth, computational efficiency is essential, so a global optimum maynot be sought. The set covering problem can be efficiently solved by agreedy heuristic as follows:

Step 0: F* = Ø; Ω* = Ω\A. Step 1: Select f such that |S_(f)| = max{|S_(j)| : j ε FA\F*} Step 2: F* = F* ∪ {f}; S_(j) = S_(j)\S_(f) for allj εFA\F*; Ω* = Ω*\S_(f); Step 3: If Ω* = Ø, STOP and output cover F*.Otherwise, go to Step 1.Generalized Set Covering Problem According to the Second Embodiment

According to this embodiment, a generalized set covering problem is usedto accomplish steps (i), (ii) and (iii), noted above with respect toprofiling or fingerprinting. The generalized set covering formulationlooks for a cover in which every element is covered k times (belongs toat least k sets). k may be defined as the depth of the cover. This modelmay be more appropriate for obtaining a robust profile, so that acustomer whose call pattern changes to some degree following a move canstill be recognized. Multi-covering allows selection of more featuresthan a regular set covering. In addition, different customers can becovered to different depths when appropriate. For example, it may bedesirable to cover customer B₁, who has a large number of features, moretimes than customer B₂, whose list of features is much smaller.

For each customer B, let k_(B) be the desired depth of coverage. Thenthe multicover formulation is as follows:

minimize

$\sum\limits_{f = 1}^{n}\; x_{f}$subject to

${\sum\limits_{f = 1}^{n}{a_{B\; f}\; x_{f}}} \geq k_{B}$for B=1, . . . , mand x_(f)=0 or 1 for f εF_(A)Cover F*={f: x_(f)=1} provides a minimal set of features establishingcustomer A as distinct from each customer B in the sample to be profiledat the level of coverage desired for robustness.

Modified Greedy Algorithm: Step 0: F* = Ø; Ω* = Ω\A Step 1: Select fsuch that |S_(f)| = max {|S_(j)| : j ε FA\F*} Step 2: F* = F* ∪ {f} Step3: For all B ε S_(f): k_(B) = k_(B) − 1; if k_(B) = 0, Ω* = Ω*\B andS_(j)=S_(j)\B for all j ε F_(A)\F* Step 4: If Ω* = Ø, STOP and outputcover F* If F* = F_(A), STOP; no cover of depth k exists. Otherwise, goto Step 1.

In FIG. 5, a feature f is shown with a line connecting it to a member ofthe sample (A, B1, B2, B3) only if f passes the threshold for thatmember. Customer A, the customer being profiled, is connected to all ofthe features. Thus, customer B1 can be covered, for example, once bychoosing any feature that has no connecting line to B1. In thefingerprint of customer A pictured in FIG. 5, coverage for each of thecustomers B1, B2, B3 is at depth 3. The greedy algorithm may firstinclude in the profile the two features (5 and 7) that are unique tocustomer A. This gives each of customers B1, B2, and B3 coverage ofdepth 2. Next, feature 1 may be included in the profile. It coverscustomers B2 and B3, which now have coverage of depth 3. Finally,feature 2 is included, which covers customers B1 and B3. Now the depthof coverage for customers B1 and B2 equals 3, while the depth ofcoverage for customer B3 equals 4. In this example, customer A has afingerprint of size 4 (marked by thicker lines).

If a customer being fingerprinted has at least K unique features (thatis, features which do not appear in the call detail of the remainingcustomers in the sample being profiled) and K≧max_(B){k_(B)}, then theset covering model may not be necessary, because a collection of Kunique features can be used for a profile. In the example pictured inFIG. 6, the fingerprint of customer A consists of 5 features, all ofwhich are unique to customer A. Customers B1, B2, B3 are all covered atthe depth of 5. This saves computing time by applying the set coveringalgorithm only in cases where there are not enough unique features.

The customer profile should be stable to be of use. In the presentexample, the customer profile may be considered as stable if, forexample, a fingerprint including at least 5 features can be found ineach month, and either at least 30% of the features remain unchangedfrom month to month or at least three features remain unchanged frommonth to month. However, the stability of a fingerprint can be definedas appropriate for the particular service provider.

Phase II: Matching Customers to Profiles

Referring again to FIG. 3, in steps S1 and S2, the phone numbers ofcustomers to be profiled, such as customer A in FIG. 4, are determined.In step S3, call details of calls over the service provider networkinvolving these customers are determined over a predetermined period oftime. In step S4, calls for a particular number appearing more than onceare aggregated into a feature, and in step S5 the appropriatealgorithms, as discussed above, are applied to choose features thatuniquely identify as many customers as possible of the customers to beprofiled. In steps S6 and S7, the phone numbers of customers to berecognized or new connect customers are determined. In step S8, the calldetails of calls over the service provider network involving new connectcustomers are determined over a predetermined period of time. Thispredetermined period of may be the same, less than or more than the timeperiod in step S3. In step S9, calls for one number are aggregated intoa feature, and in step S10, the appropriate algorithms, as discussedabove, are applied to choose features that uniquely identify as manycustomers in this group as possible. In step S11, the profiles of thecustomers from the second sample of customers being investigated arecompared with the profiles of the first sample of customers, includingcustomers A and B. When a profile in one group overlaps a profile in theother group, it is determined that there is a strong possibility of amatch in step S12, indicating that the profiles correspond to accountsbelonging to the same customer. The service provider may act on resultsindicating a strong possibility of a match by further investigating theparticular accounts and possibly contacting the customer directly.

According to the present invention, as described above with respect tothe example of a telecommunications system and a long-distance telephoneservice provider, multiple accounts belonging to a single customer maybe easily and accurately determined by the service provider. Therefore,according to the present invention, accurate results can be obtainedwithout requiring the services of an outside vendor.

While particular embodiments of the invention have been shown anddescribed, it is recognized that various modifications thereof willoccur to those skilled in the art without departing from the spirit andscope of the invention.

1. A method for tracking telecommunication customers comprising:employing a set of call detail information records to create a set offeatures for each putative customer in said set, where each putativecustomer is identified by one or more attributes, and where feature insaid set relates to calls made by said putative customer to anidentified telephone number, or made by said identified telephone numberto said putative customer; and analyzing said set of features toidentify two of putative customers with calling patterns that indicate,with a probability in excess of a preselected threshold, that theputative customers are in reality a single customer.
 2. The method ofclaim 1 where said set is composed of two sets, from two different timeintervals.
 3. The method of claim 1 were said feature is an aggregate ofcalls made by said customer to a number, or an aggregate of calls madeby said customer by said number.
 4. The method of claim 1 where said setof features is a set that corresponds to information on all calls madeby said customer, or all calls made to said customer, reduced bydiscarding calls that fail to meet a predetermined usefulness threshold.5. The method of claim 4 where said step of analyzing employs analgorithm for solving a set covering problem.
 6. The method of claim 4where said step of analyzing considers, in analyzing the features ofeach customer, only those features that are necessary to distinguishsaid customer from other customers.
 7. A method for trackingtelecommunication customers comprising: employing a first set of calldetail information records to create a set of features for each customerin said set, where each customer is identified by one or moreattributes, and where feature in said set relates to calls made by saidcustomer to an identified telephone number, or made by said identifiedtelephone number to said customer; employing a second set of call detailinformation records to create a set of features for each customer insaid set, where each customer is identified by one or more attributes,and where feature in said set relates to calls made by said customer toan identified telephone number, or made by said identified telephonenumber to said customer; analyzing said set of features created fromsaid first set and from said second set to associate customers in saidfirst set with customers in said second set, where a customer in saidfirst set is associated with a customer in said second set when acalling pattern of said customer in said first set, as evidenced by saidfeatures of said customer in said first set, and a calling pattern ofsaid customer in said second set, as evidenced by said features of saidcustomer in said second set indicate, with a probability in excess of apreselected value, that said customer in said first set and saidcustomer in said second set are one and the same customer.
 8. The methodof claim 7 were said feature is an aggregate of calls made by saidcustomer to a number, or an aggregate of calls made by said customer bysaid number.
 9. The method of claim 8 where, in connection with each ofsaid features, frequency of calls is considered.
 10. The method of claim8 where, in connection with each of said features, number of calls isconsidered.
 11. The method of claim 8 where, in connection with each ofsaid features, duration of calls is considered.
 12. The method of claim7 where said set of features is a set that corresponds to information onall calls made by said customer, or all calls made to said customer,reduced by discarding calls that fail to meet a predetermined usefulnessthreshold.
 13. The method of claim 12 where said step of analyzingemploys an algorithm for solving a set covering problem.
 14. The methodof claim 12 where said step of analyzing considers, in analyzing thefeatures of each customer, only those features that are necessary todistinguish said customer from other customers.